Recurrent neural networks are used nowadays in various fields of application as an appropriate way of modeling the changes over time of a dynamic system such that a recurrent neural network learned using training data of the dynamic system can accurately predict the observables (observable states) of the system in question. Said recurrent neural network is also used to model, as states of the dynamic system, not only the observables but also unknown hidden states of the dynamic system, wherein generally only a causal information flow, i.e. proceeding forward in time, between consecutive states is considered. However, dynamic systems are often based on the principle that future predictions concerning observables also play a role in the changes over time of the states of the system. Such dynamic systems are often only inadequately described by known recurrent neural networks.